\[\frac{c + 4}{6} = \frac{3c - 2}{7}\]
\[7 \cdot (c + 4) = 6 \cdot (3c - 2)\]
\[7c + 28 = 18c - 12\]
\[18c - 7c = 28 + 12\]
\[11c = 40\]
\[c = 40\ :11\]
\[c = 3\frac{7}{11}.\]